Algèbres différentielles de formes quasi-Jacobi d'indice nul

2025/03/26 by Dumas, François, Martin, François, Royer, Emmanuel
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.20375

Abstract

The notion of double depth associated with quasi-Jacobi forms allows distinguishing,within the algebra of quasi-Jacobi singular forms of index zero, certain significant subalgebras (modular-type forms, elliptic-type forms, Jacobi forms). We study the stability of these subalgebras under the derivations of the algebra of quasi-Jacobi singular forms of index zero and through certain sequences of bidifferential operators constituting analogs of Rankin-Cohen brackets or transvectants.

Related

• Differential algebras of quasi-Jacobi forms of index zero
• Quasimodular forms, Jacobi-like forms, and pseudodifferential operators
• Formal deformations of the algebra of Jacobi forms and Rankin-Cohen brackets
• Symmetric tensor representations,quasimodular forms, and weak Jacobi\n forms
• Modified Jacobi forms of index zero